Symbolic Algebraic Methods and Verification Methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Vienna
Springer Vienna
2001
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| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The usual usual "implementation" "implementation" ofreal numbers as floating point numbers on exist iing ng computers computers has the well-known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly. For numerical algorithms there are frequently error bounds for the computed approximation available. Traditionally a bound for the infinity norm is estima ted using ttheoretical heoretical ccoonncceeppttss llike ike the the condition condition number number of of a a matrix matrix for for example. example. Therefore Therefore the error bounds are not really available in practice since their com putation requires more or less the exact solution of the original problem. During the last years research in different areas has been intensified in or der to overcome these problems. As a result applications to different concrete problems were obtained. The LEDA-library (K. Mehlhorn et al.) offers a collection of data types for combinatorical problems. In a series of applications, where floating point arith metic fails, reliable results are delivered. Interesting examples can be found in classical geometric problems. At the Imperial College in London was introduced a simple principle for "exact arithmetic with real numbers" (A. Edalat et al.), which uses certain nonlinear transformations. Among others a library for the effective computation of the elementary functions already has been implemented |
| Physical Description: | 1 Online-Ressource (IX, 266p. 40 illus) |
| ISBN: | 9783709162804 9783211835937 |
| DOI: | 10.1007/978-3-7091-6280-4 |
Staff View
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| 500 | |a The usual usual "implementation" "implementation" ofreal numbers as floating point numbers on exist iing ng computers computers has the well-known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly. For numerical algorithms there are frequently error bounds for the computed approximation available. Traditionally a bound for the infinity norm is estima ted using ttheoretical heoretical ccoonncceeppttss llike ike the the condition condition number number of of a a matrix matrix for for example. example. Therefore Therefore the error bounds are not really available in practice since their com putation requires more or less the exact solution of the original problem. During the last years research in different areas has been intensified in or der to overcome these problems. As a result applications to different concrete problems were obtained. The LEDA-library (K. Mehlhorn et al.) offers a collection of data types for combinatorical problems. In a series of applications, where floating point arith metic fails, reliable results are delivered. Interesting examples can be found in classical geometric problems. At the Imperial College in London was introduced a simple principle for "exact arithmetic with real numbers" (A. Edalat et al.), which uses certain nonlinear transformations. Among others a library for the effective computation of the elementary functions already has been implemented | ||
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| spelling | Alefeld, Götz Verfasser aut Symbolic Algebraic Methods and Verification Methods edited by Götz Alefeld, Jiří Rohn, Siegfried Rump, Tetsuro Yamamoto Vienna Springer Vienna 2001 1 Online-Ressource (IX, 266p. 40 illus) txt rdacontent c rdamedia cr rdacarrier The usual usual "implementation" "implementation" ofreal numbers as floating point numbers on exist iing ng computers computers has the well-known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly. For numerical algorithms there are frequently error bounds for the computed approximation available. Traditionally a bound for the infinity norm is estima ted using ttheoretical heoretical ccoonncceeppttss llike ike the the condition condition number number of of a a matrix matrix for for example. example. Therefore Therefore the error bounds are not really available in practice since their com putation requires more or less the exact solution of the original problem. During the last years research in different areas has been intensified in or der to overcome these problems. As a result applications to different concrete problems were obtained. The LEDA-library (K. Mehlhorn et al.) offers a collection of data types for combinatorical problems. In a series of applications, where floating point arith metic fails, reliable results are delivered. Interesting examples can be found in classical geometric problems. At the Imperial College in London was introduced a simple principle for "exact arithmetic with real numbers" (A. Edalat et al.), which uses certain nonlinear transformations. Among others a library for the effective computation of the elementary functions already has been implemented Mathematics Computer science Algebra / Data processing Algorithms Numerical analysis Numerical Analysis Symbolic and Algebraic Manipulation Arithmetic and Logic Structures Datenverarbeitung Informatik Mathematik Computeralgebra (DE-588)4010449-7 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1999 Wadern gnd-content Computeralgebra (DE-588)4010449-7 s 2\p DE-604 Rohn, Jiří Sonstige oth Rump, Siegfried Sonstige oth Yamamoto, Tetsuro Sonstige oth https://doi.org/10.1007/978-3-7091-6280-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Alefeld, Götz Symbolic Algebraic Methods and Verification Methods Mathematics Computer science Algebra / Data processing Algorithms Numerical analysis Numerical Analysis Symbolic and Algebraic Manipulation Arithmetic and Logic Structures Datenverarbeitung Informatik Mathematik Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4010449-7 (DE-588)1071861417 |
| title | Symbolic Algebraic Methods and Verification Methods |
| title_auth | Symbolic Algebraic Methods and Verification Methods |
| title_exact_search | Symbolic Algebraic Methods and Verification Methods |
| title_full | Symbolic Algebraic Methods and Verification Methods edited by Götz Alefeld, Jiří Rohn, Siegfried Rump, Tetsuro Yamamoto |
| title_fullStr | Symbolic Algebraic Methods and Verification Methods edited by Götz Alefeld, Jiří Rohn, Siegfried Rump, Tetsuro Yamamoto |
| title_full_unstemmed | Symbolic Algebraic Methods and Verification Methods edited by Götz Alefeld, Jiří Rohn, Siegfried Rump, Tetsuro Yamamoto |
| title_short | Symbolic Algebraic Methods and Verification Methods |
| title_sort | symbolic algebraic methods and verification methods |
| topic | Mathematics Computer science Algebra / Data processing Algorithms Numerical analysis Numerical Analysis Symbolic and Algebraic Manipulation Arithmetic and Logic Structures Datenverarbeitung Informatik Mathematik Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Mathematics Computer science Algebra / Data processing Algorithms Numerical analysis Numerical Analysis Symbolic and Algebraic Manipulation Arithmetic and Logic Structures Datenverarbeitung Informatik Mathematik Computeralgebra Konferenzschrift 1999 Wadern |
| url | https://doi.org/10.1007/978-3-7091-6280-4 |
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